A knee prosthesis for replacing at least a portion of a knee joint between the distal end of a femur and the proximal end of a tibia. The knee prosthesis includes a tibial component for mounting to the proximal end of the tibia, the tibial component including a proximal surface having a semispherical medial cavity and a lateral cavity; and a femoral component for mounting to the distal end of the femur, the femoral component including a semispherical medial condylar portion for pivotally coacting with the semispherical medial cavity of the tibial component and including a semispherical lateral condylar portion for movably coacting with the lateral cavity of the tibial component; the semispherical medial condylar portion being substantially congruent with the semispherical medial cavity of the tibial component so that substantially complete surface-to-surface contact between the semispherical medial cavity of the tibial component and the semispherical medial condylar portion of the femoral component is provided throughout the range of flexion of the knee joint.